Commit c35b8a65 authored by Zhen Zhang's avatar Zhen Zhang

ticket lock

parent fcc1c439
......@@ -110,6 +110,7 @@ tests/proofmode.v
tests/barrier_client.v
tests/list_reverse.v
tests/tree_sum.v
tests/ticket_lock.v
proofmode/coq_tactics.v
proofmode/pviewshifts.v
proofmode/environments.v
......
......@@ -54,8 +54,9 @@ Section gset.
Canonical Structure gset_disjUR :=
discreteUR (gset_disj K) gset_disj_ra_mixin gset_disj_ucmra_mixin.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Arguments op _ _ _ _ : simpl never.
Section fpu.
Context `{Fresh K (gset K), !FreshSpec K (gset K)}.
Lemma gset_alloc_updateP_strong P (Q : gset_disj K Prop) X :
( Y, X Y j, j Y P j)
......@@ -98,6 +99,8 @@ Section gset.
Lemma gset_alloc_empty_updateP' : GSet ~~>: λ Y, i, Y = GSet {[ i ]}.
Proof. eauto using gset_alloc_empty_updateP. Qed.
End fpu.
Lemma gset_alloc_local_update X i Xf :
i X i Xf GSet X ~l~> GSet ({[i]} X) @ Some (GSet Xf).
Proof.
......
......@@ -56,6 +56,10 @@ Section auth.
Lemma auth_own_op γ a b : auth_own γ (a b) ⊣⊢ auth_own γ a auth_own γ b.
Proof. by rewrite /auth_own -own_op auth_frag_op. Qed.
Global Instance from_sep_own_authM γ a b :
FromSep (auth_own γ (a b)) (auth_own γ a) (auth_own γ b) | 90.
Proof. by rewrite /FromSep auth_own_op. Qed.
Lemma auth_own_mono γ a b : a b auth_own γ b auth_own γ a.
Proof. intros [? ->]. by rewrite auth_own_op sep_elim_l. Qed.
......
From iris.program_logic Require Export global_functor auth.
From iris.proofmode Require Import invariants ghost_ownership.
From iris.heap_lang Require Import proofmode notation.
From iris.algebra Require Import gset.
From iris.prelude Require Import set.
Import uPred.
Definition wait_loop: val :=
rec: "wait_loop" "x" "l" :=
let: "o" := Fst !"l" in
if: "x" = "o"
then #() (* my turn *)
else "wait_loop" "x" "l".
Definition newlock : val := λ: <>, ref((* owner *) #0, (* next *) #0).
Definition acquire : val :=
rec: "acquire" "l" :=
let: "oldl" := !"l" in
if: CAS "l" "oldl" (Fst "oldl", Snd "oldl" + #1)
then wait_loop (Snd "oldl") "l"
else "acquire" "l".
Definition release : val :=
rec: "release" "l" :=
let: "oldl" := !"l" in
if: CAS "l" "oldl" (Fst "oldl" + #1, Snd "oldl")
then #()
else "release" "l".
Global Opaque newlock acquire release wait_loop.
(** The CMRA we need. *)
Class tlockG Σ := TlockG {
tlock_G :> authG heap_lang Σ (gset_disjUR nat);
tlock_exclG :> inG heap_lang Σ (exclR unitC)
}.
Definition tlockGF : gFunctorList := [ authGF (gset_disjUR nat)
; GFunctor (constRF (exclR unitC))].
Instance inGF_tlockG `{H : inGFs heap_lang Σ tlockGF} : tlockG Σ.
Proof. destruct H as (? & ? & ?). split. apply _. apply: inGF_inG. Qed.
Section proof.
Context `{!heapG Σ, !tlockG Σ} (N : namespace).
Local Notation iProp := (iPropG heap_lang Σ).
Section natstuff.
Open Scope nat_scope.
Fixpoint natset (s len: nat) : gset nat :=
match len with
| O =>
| S len' => natset s len' {[ s + len' ]}
end.
Lemma natset_range: (len s x: nat), x natset s len -> x < (s + len).
Proof.
intros len.
elim len.
+ intros. simpl in H. set_solver.
+ intros. simpl in H0. apply elem_of_union in H0.
destruct H0.
- apply H in H0.
omega.
- assert (x = s + n).
set_solver.
omega.
Qed.
Lemma natset_not_in: x, x natset 0 x.
Proof.
intros x H.
apply natset_range in H.
omega.
Qed.
Lemma natset_incr: x, {[x]} natset 0 x = natset 0 (x + 1).
Proof.
intros.
rewrite Nat.add_1_r.
simpl.
set_solver.
Qed.
Lemma natset_disj: x, {[x]} natset 0 x.
Proof.
intros.
assert (x natset 0 x).
apply natset_not_in.
set_solver.
Qed.
End natstuff.
Definition tickets_inv (n: nat) (gs: gset_disjUR nat) :iProp :=
( gs', GSet gs' = gs gs' = natset 0 n)%I.
Definition lock_inv (γ1 γ2: gname) (l : loc) (R : iProp) : iProp :=
( (o n: nat), l (#o, #n)
auth_inv γ1 (tickets_inv n)
((own γ2 (Excl ()) R)
auth_own γ1 (GSet {[ o ]})))%I.
Definition is_lock (l: loc) (R: iProp) : iProp :=
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R))%I.
Definition issued (l : loc) (x: nat) (R : iProp) : iProp :=
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R) auth_own γ1 (GSet {[ x ]}))%I.
Definition locked (l : loc) (R : iProp) : iProp :=
( γ1 γ2, heapN N heap_ctx inv N (lock_inv γ1 γ2 l R) own γ2 (Excl ()))%I.
Global Instance lock_inv_ne n γ1 γ2 l : Proper (dist n ==> dist n) (lock_inv γ1 γ2 l).
Proof. solve_proper. Qed.
Global Instance is_lock_ne n l: Proper (dist n ==> dist n) (is_lock l).
Proof. solve_proper. Qed.
Global Instance locked_ne n l: Proper (dist n ==> dist n) (locked l).
Proof. solve_proper. Qed.
Global Instance is_lock_persistent l R : PersistentP (is_lock l R).
Proof. apply _. Qed.
Lemma newlock_spec (R : iProp) Φ :
heapN N
heap_ctx R ( l, is_lock l R - Φ #l) WP newlock #() {{ Φ }}.
Proof.
iIntros (?) "(#Hh & HR & HΦ)". rewrite /newlock.
wp_seq. wp_alloc l as "Hl".
iPvs (own_alloc (Excl ())) as (γ2) "Hγ2"; first done.
iPvs (own_alloc_strong (Auth (Excl' ) ) _ {[ γ2 ]}) as (γ1) "[% Hγ1]"; first done.
iPvs (inv_alloc N _ (lock_inv γ1 γ2 l R) with "[-HΦ]"); first done.
{ iNext. rewrite /lock_inv.
iExists 0%nat, 0%nat.
iFrame.
iSplitL "Hγ1".
{ rewrite /auth_inv.
iExists (GSet ).
iFrame.
rewrite /tickets_inv.
iExists ; by iSplit.
}
iLeft.
by iFrame.
}
iPvsIntro.
iApply "HΦ".
iExists γ1, γ2.
iSplit; by auto.
Qed.
Lemma wait_loop_spec l x R (Φ : val iProp) :
issued l x R ( l, locked l R - R - Φ #()) WP wait_loop #x #l {{ Φ }}.
Proof.
iIntros "[Hl HΦ]". iDestruct "Hl" as (γ1 γ2) "(% & #? & #? & Ht)".
iLöb as "IH". wp_rec. wp_let. wp_focus (! _)%E.
iInv N as (o n) "[Hl Ha]".
wp_load. iPvsIntro.
destruct (decide (x = o)) as [Heq|Hneq].
- subst.
iDestruct "Ha" as "[Hainv [[Ho HR] | Haown]]".
+ iSplitL "Hl Hainv Ht".
* iNext.
iExists o, n.
iFrame.
by iRight.
* wp_proj. wp_let. wp_op=>Ho; last by contradiction Ho. clear Ho.
wp_if. iPvsIntro.
iApply ("HΦ" with "[-HR] HR"). iExists γ1, γ2; eauto.
+ iExFalso. iCombine "Ht" "Haown" as "Haown".
iDestruct (auth_own_valid with "Haown") as "%".
apply gset_disj_valid_op in H0.
set_solver.
- iSplitL "Hl Ha".
+ iNext. iExists o, n. by iFrame.
+ wp_proj. wp_let. wp_op=>?.
* subst. contradiction Hneq. omega.
* wp_if. by iApply ("IH" with "Ht").
Qed.
Lemma acquire_spec l R (Φ : val iProp) :
is_lock l R ( l, locked l R - R - Φ #()) WP acquire #l {{ Φ }}.
Proof.
iIntros "[Hl HΦ]". iDestruct "Hl" as (γ1 γ2) "(% & #? & #?)".
iLöb as "IH". wp_rec. wp_focus (! _)%E.
iInv N as (o n) "[Hl Ha]".
wp_load. iPvsIntro.
iSplitL "Hl Ha".
- iNext. iExists o, n. by iFrame.
- wp_let.
wp_focus (CAS _ _ _).
wp_proj. wp_proj.
wp_op.
iInv N as (o' n') "[Hl [Hainv Haown]]".
destruct (decide ((#o', #n')%V = (#o, #n)%V)) as [Heq | Hneq].
+ wp_cas_suc.
inversion Heq; subst.
iDestruct "Hainv" as (s) "[Ho Ht]".
iDestruct (own_valid with "#Ho") as "Hvalid".
iDestruct (auth_validI _ with "Hvalid") as "[_ %]"; simpl; iClear "Hvalid".
destruct s as [s|]; last by contradiction.
iDestruct "Ht" as (gs) "[% %]".
inversion H3. subst. subst. clear H3.
iPvs (own_update with "Ho") as "Ho".
{ eapply auth_update_no_frag, gset_alloc_empty_local_update.
eapply natset_not_in. }
iDestruct "Ho" as "[Hofull Hofrag]".
iSplitL "Hl Haown Hofull".
* replace (GSet {[n']} GSet (natset 0 n')) with (GSet (natset 0 (n' + 1))).
{ iPvsIntro. iNext.
iExists o', (n' + 1)%nat.
rewrite Nat2Z.inj_add.
iFrame. iExists (GSet (natset 0 (n' + 1))).
iFrame. iExists (natset 0 (n' + 1)).
by auto.
}
{ rewrite gset_disj_union.
replace (natset 0 (n' + 1)) with ({[n']} natset 0 n').
- auto.
- apply natset_incr.
- apply natset_disj.
}
* iPvsIntro. wp_if. wp_proj.
iApply wait_loop_spec.
iSplitR "HΦ"; last by done.
iExists γ1, γ2.
(* FIXME: iFrame should be able to make progress here. *)
repeat (iSplit; first by auto).
by rewrite /auth_own.
+ wp_cas_fail.
iPvsIntro.
iSplitL "Hl Hainv Haown".
{ iNext. iExists o', n'. by iFrame. }
{ wp_if. by iApply "IH". }
Qed.
Lemma release_spec R l (Φ : val iProp):
locked l R R Φ #() WP release #l {{ Φ }}.
Proof.
iIntros "(Hl & HR & HΦ)"; iDestruct "Hl" as (γ1 γ2) "(% & #? & #? & Hγ)".
iLöb as "IH". wp_rec. wp_focus (! _)%E.
iInv N as (o n) "[Hl Hr]".
wp_load. iPvsIntro.
iSplitL "Hl Hr".
- iNext. iExists o, n. by iFrame.
- wp_let. wp_focus (CAS _ _ _ ).
wp_proj. wp_op. wp_proj.
iInv N as (o' n') "[Hl Hr]".
destruct (decide ((#o', #n')%V = (#o, #n)%V)) as [Heq | Hneq].
+ inversion Heq; subst.
wp_cas_suc.
iDestruct "Hr" as "[Hainv [[Ho _] | Hown]]".
* iExFalso. iCombine "Hγ" "Ho" as "Ho".
iDestruct (own_valid with "#Ho") as "Hvalid".
by iDestruct (excl_validI _ with "Hvalid") as "%".
* iSplitL "Hl HR Hγ Hainv".
{ iPvsIntro. iNext. iExists (o' + 1)%nat, n'%nat.
iFrame. rewrite Nat2Z.inj_add.
iFrame. iLeft; by iFrame. }
{ iPvsIntro. by wp_if. }
+ wp_cas_fail.
iPvsIntro.
iSplitL "Hl Hr".
* iNext. iExists o', n'. by iFrame.
* wp_if. by iApply ("IH" with "Hγ HR").
Qed.
End proof.
Typeclasses Opaque is_lock issued locked.
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